Stir in kimchi, kimchi liquid, stock, water, soy sauce, mirin, gochujang, and doenjang. Bring to a boil over high heat, reduce heat to a strong simmer. Stir in soft tofu and kochukaru (if using), and cook until kale is tender and soup has slightly thickened, about 10 minutes. Season to taste with more salt and chili flakes if desired.